Amazon is considering opening 3,000 of its cashierless stores by 2021, Bloomberg said in a report on Wednesday, based on conversations with people familiar with the matter. The e-commerce giant's push into retail would threaten the likes of convenience stores and fast-food chains across the U.S. selling items for customers in a pinch for time.

Amazon currently has three locations — known as Amazon Go — open in Seattle, where Amazon is headquartered, and on Monday opened a location in Chicago. The automated grocery stores promise "no lines, no checkouts, no registers." Customers simply scan their Amazon Go apps as they walk into the spaces — which are roughly 2,000 square feet — pick up whatever they want, and walk out.

"We don't comment on rumors or speculation," an Amazon spokesperson told CNBC in an emailed statement.

The existing Amazon Go stores primarily sell grab-and-go food items such as prepared sandwiches, salads, yogurt and granola bars. Amazon has also experimented with selling meal kits in some locations.

The company is planning to have about 10 Amazon Go locations open by the end of this year, according to the report, while Amazon aims to have 50 shops in "major metro areas" such as San Francisco and New York by 2019.

Still, the hurdle in opening so many Amazon Go locations would be the costs associated with such lofty expansion plans. Finding real estate wouldn't be so much of an issue, with ample store closures taking place across the U.S., leaving plenty of vacant storefronts behind.

The first Amazon Go location in downtown Seattle required more than $1 million in hardware, a person familiar with those expenses told Bloomberg. (Read the full report here.)